Appears in collections : Geometry of singular spaces and maps / Géométrie des espaces et applications singuliers, Exposés de recherche

Pham and Teissier showed in the late 60’s that any two plane curve germs with the same outer Lipschitz geometry have equivalent embeddings into $\mathbb{C}^2$. We consider to what extent the same holds in higher dimensions, giving examples of normal surface singularities which have the same topology and outer Lipschitz geometry but whose embeddings into $\mathbb{C}^3$ are topologically inequivalent. Joint work with Anne Pichon.

Keywords: bilipschitz - Lipschitz geometry - normal surface singularity - Zariski equisingularity - Lipschitz equisingularity